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# SSC CGL Tier-I 04 March 2020 Shift-III Previous Year Paper

January 1, 2021
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January 2, 2021

SSC CGL 4th March 2020 Shift-3

General Intelligence and Reasoning

Instructions

For the following questions answer them individually

Q. 1 Select the correct mirror image of the given figure when a mirror is placed on the right side of the figure.

Answer: A.

Explanation:

Option A. is the mirror image of the question figure.

∴ The correct answer is option A.

Q. 2 In a certain code language, ‘EARTH’ is coded as ‘8201815’. How will ‘ORBIT’ be coded as in that language?

A. 18172372

B. 20921815

C. 37681026

D. 17113912

Answer: B.

Explanation:

Similarly,

∴ The correct answer is option B.

Q. 3 Select the option that is related to the third term in the same way as the second term is related to the first term and sixth term is related to the fifth term.

72 : 14 :: 87 : ? :: 96 : 54

A. 56

B. 52

C. 29

D. 15

Answer: A.

Explanation:

7×2 = 14

9×6 = 54

Similarly,

8×7 = 56

∴ The correct answer is option A.

Q. 4 Select the option that depicts how the given transparent sheet of paper would appear if it is folded at the dotted line.

Answer: C.

Explanation:

The sheet will be appear as,

∴ The correct answer is option C.

Q. 5 How many rectangles are there in the given figure?

A. 15

B. 17

C. 11

D. 13

Answer: B.

Explanation:

Number of rectangles in EFHG = 1 + 2 + 3 = 6

Number of rectangles in ABCD = 1 + 2 + 3 + 4 = 10

1 rectangle is IJKL.

So, total rectangles = 6 + 10 + 1 = 17

∴ The correct answer is option B.

Q. 6 In the given Venn diagram, the ‘rectangle’ represents ‘engineers’, the ‘circle’ represents ‘managers’, and the ‘triangle’ represents ‘married’. The numbers given in the diagram represent the number of persons in that particular category.

How many people are married but are NOT engineers?

A. 29

B. 16

C. 70

D. 13

Answer: A.

Explanation:

Number of people are married but are NOT engineers = 13 + 16 = 29

∴ The correct answer is option A.

Q. 7 In a certain code language, ‘JUPITER’ is written as ‘ JVOJSFR ‘. How will ‘NEPTUNE’be written as in that language?

A. NDPSVME

B. NGOUTOE

C. NFOUTOE

D. NFOSTOE

Answer: C.

Explanation:

J = J

U + 1 = V

P – 1 = O

I + 1 = J

T – 1 = S

E + 1 = F

R = R

Similarly,

N = N

E +1 = F

P – 1 = O

T + 1 = U

U – 1 = T

N + 1 = O

E = E

‘NEPTUNE’ is written as ‘NFOUTOE’.

∴ The correct answer is option C.

Q. 8 A product was marked for sale with a label price, which is at 20% discount on the printed price. At the time of sale, the shopkeeper gave an additional 10% discount on the label price. If a customer bought the product at ₹468, then what is the printed price of the product?

A. ₹700

B. ₹650

C. ₹520

D. ₹600

Answer: B.

Explanation:

Let the printed price be 100%.

Discount = 20%

Label price = 100 – 20 = 80%

Additional discount = 10%

Selling price = 100 – 10 = 90% of label price = 80 ×90/100= 72%

72% = 468

Printed price(100%) =650/ 72 ×100 = 650

Q. 9 A + B means ‘A. is the wife of B’;

A B means ‘B. is the daughter of A’;

A × B means ‘B. is the brother of A’;

A ÷ B means ‘A. is the father of B’.

If,  P + R × T Q + S ÷ U , then how is P it related to the mother of  U

A. Maternal grandmother

B. Mother

C. Paternal grandmother

D. Aunt

Answer: D.

Explanation:

In the diagram, Circle shows the female, square shows the male, vertical lines show the generation, single horizontal line shows the brother/sister and double horizontal lines show the couple.

From the diagram,

Mother of ‘U’ is aunt of the ‘P’.

Q. 10 Arrange the following words in a logical and meaningful order (according to population).

1. Andhra Pradesh

2. Madhya Pradesh

3. Arunachal Pradesh

4. Uttar Pradesh

5. Himachal Pradesh

A. 4-1-2-3-5

B. 4-2-1-5-3

C. 4-1-2-5-3

D. 4-2-1-3-5

Answer: B.

Explanation:

State According to population,

Uttar Pradesh, Madhya Pradesh, Andhra Pradesh, Himachal Pradesh, Arunachal Pradesh

∴ The correct answer is option B.

Q. 11 Select the option in which the words share the same relationship as that shared by the given pair of words. Dentist : Doctor

A. Line : Circle

B. Algebra : Geometry

C. Chemistry : Science

D. Biology : Astrology

Answer: C.

Explanation:

Dentist come under the doctor similarly,

Chemistry come under the chemistry.

∴ The correct answer is option C.

Q. 12 Which two signs should be interchanged to make the given equation correct? 121 + 11 − 42 × 6 ÷ 7 = 83

A. and÷

B. +and÷

C. ÷and×

D. ×and−

Answer: C.

Explanation:

121 + 11 − 42 × 6 ÷ 7 = 83

From the option C,

121 + 11 − 42 ÷ 1/6 × 7 = 83

121 + 11 − 42 ÷ 6 × 7 = 83

121 + 11 − 49 = 83

83 = 83

∴ The correct answer is option C.

Q. 13 Select the option in which the given figure is embedded (rotation is not allowed).

Answer: A.

Explanation:

The question figure is shown by red line

∴ The correct answer is option A.

Q. 14 Select the figure that can replace the question mark (?) in the following series.

Answer: C.

Explanation:

In the each figure, pentagon and arrow rotate 180° in each step and figure are also rotate 90° in anti clock direction so, Next step,

∴ The correct answer is option C.

Q. 15 Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.

A. 10 : 123

B. 17 : 290

C. 14 : 227

D. 11 : 146

Answer: B.

Explanation:

In 10 : 123,

(10 + 1)2 + 2

= 121 + 2 = 123

In 17 : 290,

(17 + 1)2 + 2

= 324 – 34 = 290

In 14 : 227,

(14 + 1)2 + 2

= 225 + 2 = 227

In 11 : 146,

(11 + 1)2 + 2

= 144 + 2 = 146

∴ The correct answer is option B.

Q. 16 Select the option in which the number set shares the same relationship as that shared by the given number set. (17, 24, 45)

A. (18, 23, 46)

B. (19, 26, 34)

C. (15, 20, 43)

D. (12, 19, 40)

Answer: D.

Explanation:

In (17, 24, 45),

17 + 7 = 24 + 21 = 45

Similarly,

From (12, 19, 40),

12 + 7 = 19 + 21 = 40

∴ The correct answer is option D.

Q. 17 Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement(s).

Statements:

All singers are dancers.

No dancer is a plumber.

Conclusions:

I. No plumber is a singer.

II. Some singers are plumbers.

III. Some dancers are singers.

A. Only conclusion I follow.

B. Only conclusions II and III follow.

C. Only conclusions I and III follow.

D. Only conclusion II follows.

Answer: C.

Explanation:

From the Venn diagram,

Only conclusions I and III follow.

∴ The correct answer is option C.

Q. 18 Select the number that can replace the question mark (?) in the following series.

1537, 1539, 1543, ?, 1557, 1567

A. 1553

B. 1550

C. 1546

D. 1549

Answer: D.

Explanation:

The series follows pattern as,

1537 + 2 = 1539

1539 + 4 = 1543

1543 + 6 = 1549

1549 + 8 = 1557

1567 + 10 = 1577

∴ The correct answer is option D.

Q. 19 Four words have been given, out of which three are alike in some manner and one is different. Select the odd word.

A. Hyderabad

B. Aurangabad

C. Chennai

D. Gangtok

Answer: B.

Explanation:

Except option B, remaining all are capitals.

Q. 20 Select the letter-cluster that can replace the question mark (?) in the following series.

DAG, FCI, ? , JGM, LIO

A. GDJ

B. IFL

C. HKE

D. HEK

Answer: D.

Explanation:

The series follows pattern as,

(D + 2)(A + 2)(G + 2) = FCI

(F + 2)(C + 2)(I + 2) = HEK

(H + 2)(E + 2)(K + 2) = JGM

(J + 2)(G + 2)(M + 2) = LIO

∴ The correct answer is option D.

Q. 21 ‘Wheat’ is related to ‘Bread’ in the same way as ‘Sugarcane’ is related to ‘………………’

A. Jaggery

B. Mayonnaise

C. Grass

D. Ketchup

Answer: A.

Explanation:

‘Bread’ made by ‘Wheat’ similary,

‘Jaggery’ Made by ‘Sugarcane’.

∴ The correct answer is option A.

Q. 22 Four Letter-clusters have been given, out of which three are alike in some manner and one is different. Select the odd letter-cluster.

A. FGL

B. ABF

C. IJN

D. MNR

Answer: A.

Explanation:

F + 1 = G + 5 = L

A + 1 = B + 4 = F

I + 1 = J + 4 = N

M + 1 = N + 4 = R

So, option A. is odd.

∴ The correct answer is option A.

Q. 23 Select the letter that can replace the question mark (?) in the following series.

A, E, J, ?, W

A.

B.

C.

D.

Answer: B.

Explanation:

The series follows pattern as,

A + 4 = E

E + 5 = J

J + 6 = P

P + 7 = W

∴ The correct answer is option B.

Q. 24 Three different positions of the same dice are shown. Select the symbol that will be on the face opposite to the one showing ‘ = ’.

A.

B.

C.

D.

Answer: A.

Explanation:

From last 2 figures,

‘%’ = ‘%’

‘\$’ = ‘=’

‘*’ = ‘+’

Opposite face of ‘=’ = ‘\$’

∴ The correct answer is option A.

Q. 25 Study the given pattern carefully and select the number that can replace the question mark (?) in it.

A. 64

B. 96

C. 82

D. 74

Answer: D.

Explanation:

4 + 6 = 10

10 + (6 + 4 = 10) = 20

20 + (10 + 4 = 14) = 34

34 + (14 + 4 = 18) =52

52 + (18 + 4 = 22) = 74

74 + (22 + 4 = 26) = 100

100 + (26 + 4 = 30) = 130

∴ The correct answer is option D.

General Awareness

Instructions

For the following questions answer them individually

Q. 26 Four multi-storied illegal constructions – Jain Coral Cove, H20 Holy Faith, Alfa Serene and Golden Kayaloram – were razed to the ground in January 2020 following Supreme Court instructions. In which state did this happen?

A. Karnataka

B. Goa

C. Kerala

D. Tamil Nadu

Answer: C.

Q. 27 Name the company that has acquired an online travel portal Yatra Online Inc., for an enterprise value of \$337.8 million, in an all-stock transaction.

A. Make my trip.com

B. Trivago

C. Ebix Inc.

D. Trip Advisor

Answer: C.

Q. 28 Which of the following is an INCORRECT sequence of Mughal rulers?

A. Jahangir, Shah Jahan, Aurangzeb

B. Akbar, Shah Jahan, Jahangir

C. Babur, Humayun, Akbar

D. Akbar, Jahangir, Shah Jahan

Answer: B.

Q. 29 The recently revoked ‘Article 370’ is associated with which of these states of India?

A. Assam

B. Sikkim

C. Nagaland

D. Kashmir

Answer: D.

Q. 30 Bhavai and Kalbelia as traditional dance forms, owe their genesis to which Indian state?

A. Punjab

B. Rajasthan

C. Assam

D. Odisha

Answer: B.

Q. 31 Iranian Major General Qasem Soleimani was recently (2020) assassinated by the US military in ______.

A. United Arab Emirates

B. Iraq

C. Saudi Arabia

D. Pakistan

Answer: B.

Q. 32 Who is the only scientist in the world to have won the Nobel prize in Chemistry twice?

A. Linus Carl Pauling

B. Roger D. Kornberg

C. Madame Curie

D. Frederick Sanger

Answer: D.

Q. 33 The American scientist Edwin Hubble’s name is associated with which of these theories?

A. Lattice Gauge Theory

B. Quantum Chromodynamics Theory

C. Partial Coherence of Light Theory

D. The Big Bang Theory

Answer: D.

Q. 34 The city of Vijayawada lies on the banks of which of these rivers?

A. Mahanadi

B. Tapti

C. Krishna

D. Godavari

Answer: C.

Q. 35 Only one Indian batsman has scored a triple century in test cricket other than Virender Sehwag. Name this batsman.

A. Ajinkya Rahane

B. Rohit Sharma

C. Shikhar Dhawan

D. Karun Nair

Answer: D.

Q. 36 What is the name of the phenomena in physics and astronomy which involves the splitting of a spectral line into two or more components of slightly different frequency when the light source is placed in a magnetic field?

A. Lumen Effect

B. Alpenglow Effect

C. Zeeman Effect

D. Raman Effect

Answer: C.

Q. 37 When does the entire earth experience equal days and nights?

A. Day of winter solstice

B. Day of summer solstice

C. At orbital plane

D. Day of equinox

Answer: D.

Q. 38 Who among the following is the current (January 2020) Governor of Kerala?

A. Arif Mohammed Khan

B. Satya Pal Mallik

C. Lalji Tandon

D. B.D. Mishra

Answer: A.

Q. 39 Name the two Indian actors who shared the National Best Actor Award (Male) in the 66th National Film Awards 2019.

A. Ayushmann Khurrana and Vicky Kaushal

B. Ranbir Kapoor and Akshay Kumar

C. Nana Patekar and Mohanlal

D. Amitabh Bachchan and Ranbir Kapoor

Answer: A.

Q. 40 Former union minister and former Karnataka CM, D.V. Sadananda Gowda is a cabinet minister in the current central cabinet (February-2020). What is his portfolio?

A. Law and Justice

B. Chemicals and Fertilizers

C. Public Distribution

D. Tribal Affairs

Answer: B.

Q. 41 Who among the following is known as the ‘father of Muslim renaissance’ in Bengal?

A. Sir Sayed Ahmed Khan

B. Ameer Ali

C. Nawab Abdul Latif Khan

D. Nawab Salimullah Khan

Answer: C.

Q. 42 Name the author of the 2019 released book – ‘The Scent of God’.

A. Nayantara Sehgal

B. Githa Hariharan

C. Saikat Majumdar

D. Himanjali Sankar

Answer: C.

Q. 43 What is the name of the phenomena (driven by the scattering of light) in which mountain tops acquire a rosy or orange hue around sunrise and sunset?

A. Brillouin scattering

B. Circle of confusion

C. Alpenglow

D. Barrel distortion

Answer: C.

Q. 44 How many members did the International Monetary Fund (IMF) have as of January 2020?

A. 164

B. 174

C. 189

D. 182

Answer: C.

Q. 45 The 3rd Khelo India Youth Games 2020 is hosted by which Indian state?

A. Assam

B. Kerala

C. Karnataka

D. Punjab

Answer: A.

Q. 46 From which of the following states does 2019 Padma Vibhushan winner, Teejan Bai hail?

A. Chhattisgarh

B. Gujarat

C. Odisha

D. Telangana

Answer: A.

Q. 47 Which of these is the energy conversion that happens in the process called photosynthesis?

A. Potential energy to chemical energy

B. Light energy to chemical energy

C. Heat energy to chemical energy

D. Heat energy to light energy

Answer: B.

Q. 48 Who was the then Governor-General of British India, when ‘Sati Pratha’ became illegal and punishable?

A. Lord Cornwallis

B. Lord Wellesley

C. Lord William Bentinck

D. Warren Hastings

Answer: C.

Q. 49 Which of the following is an Indian Research Station in the Antarctica Region?

A. Orcadas

B. Maitri

C. Hope Bay

D. Mawson

Answer: B.

Q. 50 Who is the author of the delightful and anecdotal history of Indian cricket titled – ‘A Corner of a Foreign Field: The Indian History of a British Sport’?

A. Sanjay Singh

B. Ramachandra Guha

C. Bipin Chandra

D. Romila Thapar

Answer: B.

Quantitative Aptitude

Instructions

For the following questions answer them individually

Q. 51 The given table represents the production of different types of motorcycles (in thousands)over a period of six years. Study the table carefully and answer the question that follows.

During 2015, the production of which type of motorcycle was more than 25% of the total production of all types of motorcycles in 2017?

A.

B.

C.

D.

Answer: D.

Explanation:

Total production of all types of motorcycles in 2017 = 80 + 96 + 100 + 104 = 380

25% of the total production of all types of motorcycles in 2017 = 380×25/100 = 95

During 2015, the production of D. type of motorcycle was more than 25% of the total production of all types of motorcycles in 2017

Q. 52 The average age of a number of persons in a group was calculated as 35 years, which was 2.5 years more than the correct average as there was an error in recording the age of two persons as 38.5 years and 40 years instead of 29 years and 22 years respectively. The number of persons in the group was:

A. 11

B. 12

C. 15

D. 13

Answer: A.

Explanation:

Let the number of persons be x.

Wrong average = 35

Total age for wrong average = 35x

Correct average = 35 – 2.5 = 32.5

Total age for correct average = 32.5x

Correct age of two persons = 29 + 22 = 51

Wrong age of two persons = 38.5 + 40 = 78.5

Difference = 78.5- 51

35x – 32.5x = 27.5

x = 27.5/2.5 = 11

Q. 53 If sec θ + tan θ = p, 0< θ < 90, then (p2 −1) /(p2 +1) is equal to:

A. cosec θ

B. sin θ

C. cos θ

D. 2 cosec θ

Answer: B.

Explanation:

sec θ + tan θ =

(sec θ + tan θ)2 = p2  —(1)

(p2 −1) /(p2 +1)

From eq(1),

Q. 54 The chords AB and CD of a circle intersect at E. IfAE = 12 cm, BE = 20.25 cm and CE = 3 DE,thenthe length (in cm) of CE is:

A. 27

B. 25.5

C. 18

D. 28.5

Answer: A.

Explanation:

By the property,

AE × EB. = DE × CE

12 × 20.25 = DE × 3DE

243 = 3DE2

DE2 = 81

DE = 9 cm

CE = 3DE = 3 × 9 = 27 cm

Q. 55 If x + y + z = 3, and x2 + y2 + z= 101, then what is the value of √(x3 + y3 + z3 − 3xyz)

A. 19

B. 21

C. 24

D. 28

Answer: B.

Explanation:

x³ + y³ + z³ – 3xyz = (x+y+z) [(x + y + z)² – 3(xy + yz + zx)] —(1)

And,

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

On put the values,

32 = 101 + 2(xy + yz + zx

(xy + yz + zx) = -92/2 = -46

From the eq(1),

x³ + y³ + z³ – 3xyz = (3) [(3)² – 3(-46)] = 3 × 147 = 441

√(x3  + y3  + z3  − 3xyz )441 = 21

Q. 56 If 12x2 − 21x + 1 = 0, then what is the value of 9x2 + (16x2) −1

A. 429/

B. 465/16

C. 417/16

D. 453/8

Answer: C.

Explanation:

12x2 − 21x + 1 = 0

Divide by 4x,

3x − 21/4 + 1/4x = 0

3x + 1/4x = 21/4

On taking square,

(3x + 1/4x)2 = (21/4)2

9x2 + 1/16x2 + 2.3x.1/4x = 441/16

9x2 + 1/16x2 = 441/16 -3/4

9x2 + 1/16x2 = 417/16

Q. 57 A sum of ₹ x was divided between A, B, C and D in the ratio ⅓ :1/5  :1/6 :1/9. If the difference between the shares of B. and D. is ₹832, then the value of x is:

A. ₹7,592

B. ₹7,384

C. ₹7,696

D. ₹7,488

Answer: A.

Explanation:

Ratio of A, B, C and D =⅓ :1/5  :1/6 :1/9 = 30 : 18 : 15 : 10

Let the share of A, B, C. and D. be 30p, 18p, 15p and 10p.

The difference between the shares of B. and D. = 832

18p – 10p = 832

p = 832/8 = 104

x = 30p + 18p + 15p + 10p = 73p

x = 73×104 = Rs.7592

Q. 58 The area of a field in the shape of a regular hexagon is 2400√3m2. The cost of fencing the field at ₹16.80/metre is:

A. ₹4,536

B. ₹3,024

C. ₹4,032

D. ₹3,528

Answer: C.

E

xplanation:

Area of a hexagon = (3√3 a2 )/2

a= side

2400√3 = (3√3 a2 )/2

a2 = 1600

a = 40 m

Perimeter = 6a = 6×40 = 240 m

The cost of fencing the field = 240×16.8 = Rs.4032

Q. 59 Places A and B are 144 km apart. Two cars start simultaneously, one from A and the other from B If they move in the same direction, they meet after 12 hours, but if they move towards each other they meet after  9/8 hours. The speed (in km/h)of the car moving at a faster speed, is:

A. 70

B. 72

C. 60

D. 64

Answer: A.

Explanation:

Speed of faster car = v1

Speed of slower car = v2

Case I: Cars travel in same direction

144 km distance covered in 12 hours so,

Relative speed = v1 – v2

v1 – v2 = 144/12 = 12 —(1)

Case II: Cars in opposite direction

144 km distance covered in  9/8 hours so,

Relative speed = v1 + v2

v1 + v2 =144/ 9/8= 128 —(2),

From eq(1) and (2),

2v1 = 12 + 128

v1 = 140/2 = 70 km/hr

The speed of faster car is 70 km/hr.

Q. 60 A, B and C donate 8%, 7% and 9%,of their salaries, respectively to a charitable trust. The salaries of A and B are same and the difference between their donations is ₹259. The total donation of A and B is ₹1,185 more than that of C. The total donation of A and C is what percentage of the total salaries of A, B and C? (Correct to one decimal place)

A. 6.2%

B. 5.8%

C. 6.4%

D. 7.1%

Answer: B.

Explanation:

Let the salaries of A, B and C be x, x, y.

Donation of A, B and C = 0.08x, 0.07x and 0.09z

Difference between donations of A and B = 259

0.08x – 0.07x = 259

x = 259/0.01 = 25900

Total donation of A and B = donation of A + 1185

0.08x + 0.07x = 0.09z + 1185

0.15x = 0.09z + 1185

0.09z = 0.15×25900 – 1185 = 2700

z = 2700/0.09 = 30000

Total donation of A and C = 0.08x + 0.09z

=0.08×25900 + 2700 = 2072 + 2700 = 4772

Total salaries of A, B and C = 25900 + 25900 +30000 = 81800

Required percentage = 4772/81800× 100 = 5.8%

Q. 61 Four men and 6 women can complete a certain piece of work in 5 days whereas three men and 4 women can complete it in 7 days. How many men should assist 25 women to complete 2 ½ times the same work in 5 days?

A.

B. 10

C.

D.

Answer: D.

Explanation:

Total work = number of (man\woman)

Four men and 6 women can complete a certain piece of work in 5 days whereas three men and 4 women can complete it in 7 days so,

(4m + 6w) ×5 = (3m + 4w) × 7

20m + 30w = 21m + 28w

m = 2w

Now,

Work = 2½ times the same work

Work = 5/2× same work

(m/w)× 5 = 5/2 ×(4m+6w)× 5

w× 5 = 5/2 ×(4×2w+6w)× 5

w× 5 = 5/2 ×14w× 5

w = 35

So need for worker = 25w + 10w

Number of man = 10 m/2 = 5 man

Q. 62 In ABC, ∠B = 72and C = 44. Side BC is produced to D. The bisectors of B and ACD meet at E. What is the measure of BEC

A. 58

B. 46

C. 32

D. 36

Answer: C.

Explanation:

In △ABC

A + ∠B + ∠C = 180°

A = 180 − 72 − 44 = 64°

By angle bisector property,

BEC = ∠A / 2

BEC = 64° / 2 = 32°

Q. 63 In ABC, AC = 8.4cm and BC = 14cm. P is a point on AB. such that CP= 11.2 cm and ACP = ∠B. What is the length (in cm) of BP?

A. 4.12

B. 2.8

C. 3.78

D. 3.6

Answer: C.

Explanation:

ΔACP ~ ΔABC

∵ ∠ACP = ∠B ( A is common and )

BP = AB. – AP = 10.5 – 6.72 = 3.78 cm

Q. 64 If 2x2 + y2 + 8z2 − 2 2xy + 4 2yz − 8zx = (Ax + y + Bz)2 , then the value of (A2 + B2 AB) is:

A. 16

B. 14

C.

D. 18

Answer: C.

Explanation:

2x2 + y2 + 8z2 − 2√2xy + 4√2yz − 8zx = (Ax + y + Bz)2

= 2x2 + y2 + 8z2 + 2(−√2xy − 2√2yz + 4zx) = (Ax + y + Bz)2

= 2x2 + y2 + 8z2 + 2(−√2x.y y.2√2z + 2x.2√2z) = (Ax + y + Bz)2

= (+√2x y + 2√2z)2 = (Ax + y + Bz)2

Ax = √2x

A = √2

y = -1

B = 2√2

Now,

(A2 + B2 AB

((√2)2 + (2√2)2 − √2.2√2)

= 2 + 8 – 4 = 6

Q. 65 How many numbers are there from 200 to 800 which are neither divisible by 5 nor by 7?

A. 407

B. 410

C. 413

D. 411

Answer: D.

Explanation:

Total numbers = (800 – 200) + 1 = 601

Number of terms which divide by 5

l = 800

a = 200

Common difference(d) = 5

l = a + (n-1)d

800 = 200 + (n – 1)5

n-1 = 120

n = 121

Number of terms which divide by 7

l = 798

a = 203

Common difference(d) = 7

l = a + (n-1)d

798 = 203 + (n – 1)7

n-1 = 85

n = 86

Number of terms which divide by 5 and 7

l = 770

a = 210

Common difference(d) = 35

l = a + (n-1)d

770 = 210 + (n – 1)35

n-1 = 16

n = 17

Number of terms which divide by either 5 or 7 = 121 + 86 – 17 = 190 Number of terms which divide by neither 5 nor 7 = 601 – 190 = 411

Q. 66 The value of  is:

A. 17/8

B. 8/3

C. 16/170

D. 2/17

Answer: B.

Explanation:

Instructions

The given table represents the production of different types of motorcycles (in thousands) over a period of six years. Study the table carefully and answer the question that follows.

Q. 67 What is the percentage increase in the total production of all types of motorcycles from 2014 to 2018?

A. 14 3/7

B. 17 1/3

C. 16 2/3

D. 14 2/7

Answer: C.

Explanation:

Total production of all types of motorcycles in 2014 = 84 + 87 + 89 + 100 = 360 Total production of all types of motorcycles in 2018 = 98 + 92 + 110 + 120 = 420 = 420−360/360 × 100 = 60/360 × 100 =16 ⅔.

Q. 68 By what percentage is the total production of type A. motorcycles over six years, less than the total production of all types of motorcycles in 2013 and 2016?

A. 32.2

B. 32.8

C. 31.6

D. 30.5

Answer: D.

Explanation:

Total production of type A. motorcycles over six years = 95+ 84 + 85 + 89 + 80 + 98 = 531

total production of all types of motorcycles in 2013 and 2016 = 95+ 98 + 104 + 103 + 89 + 88 + 92 + 95 = 764

Required percentage =764−531/764 ×100 =233/764 ×100 =  30.5%

Instructions

For the following questions answer them individually

Q. 69 Two circles of radii 7 cm and 5 cm intersect each other at A. and B, and the distance between their centers is 10 cm. The length (in cm) of the common chord AB is:

A. (3√66 )/5

B. (4√66)/5

C. (2√74)/ 5

D. (3√74)/ 5

Answer: B.

Explanation:

AP = 5 cm

AQ = 7 cm

PQ = 10 cm

Let the CQ be x. So,

PC = 10 – x cm

△ACQ is right angle triangle so,

(AQ)2 = (AC)2 + (CQ)2

(7)2 = (AC)2 + (x)2

(AC)2 = 49 − (x)2 —(1)

△APC is right angle triangle so,

(AP)2 = (AC)2 + (PC)2

(5)2 = (AC)2 + (10 − x)2

(AC)2 = 25 − (10 − x)2 —(2)

From eq(1) and (2)

49 − (x)2 = 25 − (10 − x)2

24 − (x)2 = −(10 − x)2

(x)2 = 24 + 100 + x2 − 20

20x = 124

x = 124/20 = 6.2 cm

From eq(1),

(AC)2 = 49 − (6.2)2

(AC)2 = 49 − 38.44

(AC)2 = 10.56 = 1056/100 = 264/25

AC = (2√66)/5

The common chord AB = 2 ×(2√66)/5 = (4√66)/5

Q. 70 If the selling price of an article is 8% more than the cost price and the discount offered is 10% on the marked price of the article, then what is the ratio of the cost price to the marked price?

A. 5 : 6

B. 8 : 9

C. 3 : 4

D. 4 : 5

Answer: A.

Explanation:

Profit = 8%

Let the cost price be Rs.100.

Selling price = 108

Discount on marked price = 10% so,

selling price = 100 – 10 = 90%

90% = 108

Marked price(100%) =108/ 90 ×100 = Rs.120

Ratio of the cost price to the marked price = 100 : 120 = 5 : 6

Q. 71 The given table represents the production of different types of motorcycles (in thousands) over a period of six years. Study the table carefully and answer the question that follows.

What is the ratio of the total number of motorcycles of type B. produced in 2016 and 2018 to the total number of motorcycles of type D. produced in 2013, 2015 and 2016?

A. 1 : 2

B. 3 : 4

C. 3 : 5

D. 2 : 3

Answer: C.

Explanation:

Total number of motorcycles of type B. produced in 2016 and 2018 = 88 + 92 = 180

Total number of motorcycles of type D. produced in 2013, 2015 and 2016 = 103 + 102 + 95 = 300

Ratio of the total number of motorcycles of type B. produced in 2016 and 2018 to the total number of motorcycles of type D. produced in 2013, 2015 and 2016 = 180 : 300 = 3:5

Q. 72 A sum of ₹8,000 invested at 10% p.a. amounts to ₹9,261 in a certain time, interest compounded half-yearly. What will be the compound interest (in ₹) on the same sum for the same time at double the earlier rate of interest, when interest is compounded annually?

A. ₹2,520

B. ₹2,480

C. ₹2,560

D. ₹2,500

Answer: C.

Explanation:

for half yearly,

rate(r) = 10/2 = 5

p = 8000

Amount = 9261

Amount = p(1 + r/100 )t

9261 = 8000(1 +5/100 )t

(9261)/(8000) =(105/100 )t

(21/20)3 =(21/20 )t

t = 3 years

Time = 3/2 years

Now,

r1 = 2r = 2 ×10= 20

Compound interest = p(1 + r/100 )t − p

= 8000(1 +20/100 )3/2 − 8000

= 8000×6/5×(6/5)1/2 − 8000

= 10560 – 8000 = Rs.2560

Q. 73 A sells an article to B. at a loss of 20%, B sells it to C at a profit of 12.5% and sells it to D at a loss of 8%. If D buys it for ₹248.40, then what is the difference between the loss incurred by A and C?

A. ₹36.80

B. ₹38.40

C. ₹42.60

D. ₹39.20

Answer: B.

Explanation:

Cost price for D = 248.40

Loss for C = 8%

Cost price for C = 248.40 × 100/92 = 270

Loss of C = 270 – 248.4 = 21.6

Selling price for B = Rs. 270

Profit = 12.5%

Cost price for B = 270 ×100/112.5 = 240

Selling price for A = Rs. 240

Loss = 20%

Cost price for A = 240 × 100/80= 300

Loss for A = 300 – 240 = 60

Difference between the loss incurred by A and C = 60 – 21.6 = Rs. 38.4

Q. 74 If 7 cos2 θ + 3 sin2 θ = 6, 0< θ < 90 , then the value of (cot2 2θ+sec2 2θ)/(tan2 2θ−sin2 2θ) is:

A. 52/27

B. 26/15

C. 28/27

D. 49/45

Answer: A.

Explanation:

7 cos2θ + 3 sin2θ = 6

7(1 − sin2θ) + 3 sin2θ = 6 .

7 −7 sin2θ + 3 sin2θ = 6

4 sin2 θ = 1

sin θ = ½

( For 0< θ < 90 ,)

θ = 30

Q. 75 The value of [(cos 9+ sin 81)(sec 9 + cosec 81)]/(2sin63 + 1+ 2 sin27)is:

A. ½

B. 4/3

C. 2

D. 1

Answer: B.

Explanation:

English Comprehension

Instructions

For the following questions answer them individually

Q. 76 Select the most appropriate option to fill in the blank.

Being a millionaire, he is leading a ______ life.

A. expensive

B. conducive

C. destitute

D. luxurious

Answer: D.

Q. 77 Select the most appropriate ANTONYM of the given word.

Sparse

A. Costly

B. Tranquil

C. Scanty

D. Abundant

Answer: D.

Q. 78 Select the correct passive form of the given sentence.

Did the problems you had to face discourage you?

A. Are you being discouraged by the problems you had to face?

B. Have you been discouraged by the problems you have to face?

C. Are you discouraged by the problems you had to face?

D. Were you discouraged by the problems you had to face?

Answer: D.

Q. 79 Select the word which means the same as the group of words given.

One who is preoccupied with his own interests

A. Egoist

B. Pessimist

C. Atheist

D. Optimist

Answer: A.

Q. 80 Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order.

A. Upon returning from his travels, he was forced to live in a house where his large family lived.

B. Vaikom Muhammad Basheer was a Malayalam fiction writer from Vaikom in Kerala.

C. The household was always noisy and full of chaos, no place for a writer surely!

D. Apart from family members, myriads of domestic animals also treated the house as their own.

A. BCAD

B. BCDA

C. BADC

D. BDCA

Answer: C.

Q. 81 Select the INCORRECTLY spelt word.

A. Ignorance

B. Influence

C. Itinerent

D. Impeach

Answer: C.

Instructions

In the following passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.

Comprehension:

Milton Hershey returned to the village where he had been born, in the heart of dairy country. He opened his chocolate manufacturing plant (1)______ 1905. With access to all the fresh milk he (2)______, he began producing the finest milk chocolate. The plant (3)______ opened in a small Pennsylvania village is today the (4)______ chocolate factory in the world. The confections created here are (5)______ around the world.

Q. 82 Select the most appropriate option to fill in blank 1.

A. to

B. at

C. in

D. on

Answer: C.

Q. 83 Select the most appropriate option to fill in blank 2.

A. considered

B. kneaded

C. distributed

D. needed

Answer: D.

Q. 84 Select the most appropriate option to fill in blank 3.

A. that

B. when

C. who

D. what

Answer: A.

Q. 85 Select the most appropriate option to fill in blank 4.

A. large

B. most largest

C. largest

D. larger

Answer: C.

Q. 86 Select the most appropriate option to fill in blank 5.

A. choices

B. favourites

C. collections

D. selections

Answer: B.

Instructions

For the following questions answer them individually

Q. 87 Select the most appropriate option to fill in the blank.

Children under five years are ______ from passport biometrics.

A. acquitted

B. exempted

C. escaped

D. allowed

Answer: B.

Q. 88 Select the word which means the same as the group of words given.

A. geometrical figure with eight sides

A. Octagon

B. Pentagon

C. Hexagon

D. Heptagon

Answer: A.

Q. 89 Select the most appropriate meaning of the given idiom.

Bring to light

A. Reveal clearly

B. Cheer someone

C. Praise in public

D. Brighten up

Answer: A.

Q. 90 Select the most appropriate synonym of the given word.

Fury

A. Sin

B. Risk

C. Anger

D. Crime

Answer: C.

Q. 91 Select the most appropriate meaning of the given idiom.

Hold water

A. To be fickle

B. To be busy

C. To be valid

D. To be deep

Answer: C.

Instructions

Select the most appropriate option to substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No substitution’.

Q. 92 Your advice will benefit to me.

A. benefit from me

B. benefit me

C. No substitution

D. benefit for me

Answer: B.

Q. 93 Where you left your bag yesterday?

A. No substitution

B. Where did you left

C. Where were you leaving

D. Where did you leave

Answer: D.

Instructions

For the following questions answer them individually

Q. 94 Select the most appropriate ANTONYM of the given word.

Friendship

A. Enmity

B. Amity

C. Slavery

D. Arrogance

Answer: A.

Q. 95 Select the correct indirect form of the given sentence.

The lawyer said to me, “There is no proof of your involvement in this case.”

A. The lawyer told that there is no proof of my involvement in that case.

B. The lawyer told me that there was no proof of my involvement in that case.

C. The lawyer told me that there is no proof of your involvement in this case.

D. The lawyer said me that there was no proof of my involvement in this case.

Answer: B.

Instructions

In the sentence identify the segment which contains the grammatical error.

Q. 96 I am believing you have submitted all the necessary documents.

A. I am believing

B. necessary documents

C. you have submitted

D. all the

Answer: A.

Q. 97 No sooner did we receive your message when we heaved a sigh of relief.

A. did we receive

B. a sigh of relief

C. your message

D. when we heaved

Answer: D.

Instructions

For the following questions answer them individually

Q. 98 Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order.

A. Even the most ill-equipped laboratory would have been better than their shed.

B. Thus, they did not allow any difficulties to come in their way.

C. But their mind was set upon the discovery of radium.

D. The Curies had to work in extreme poverty.

A. DACB

B. ABCD

C. ADBC

D. DBCA

Answer: A.

Q. 99 Select the most appropriate synonym of the given word.

Solitary

A. Singular

B. Stubborn

C. Splendid

D. Sensible

Answer: A.

Q. 100 Select the INCORRECTLY spelt word.

A. Diliver

B. Denial

C. Decision

D. Deter

Answer: A.

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